With strict environmental regulations, gas turbine emissions have been heavily constrained. This requires operating conditions wherein thermo-acoustic flame instabilities are prevalent. During this process the combustor acoustics and combustion heat release fluctuations are coupled and can cause severe structural damage to engine components, reduced operability, and inefficiency that eventually increase emissions. In order to develop an engine without these problems, there needs to be a better understanding of the physics behind the coupling mechanisms of this instability. Among the several coupling mechanisms, the “velocity coupling” process is the main focus of this thesis. The majority of literature has treated axisymmetric disturbance fields which are typical of longitudinal acoustic forcing and axisymmetric excitation of ring vortices. Two important non-axisymmetric disturbances are: (1) transverse acoustics, in the case of circumferential modes of a multi-nozzle annular combustor and (2) helical flow disturbances, seen in the case of swirling flow hydrodynamic instabilities. With significantly less analytical treatment of this non-axisymmetric problem, a general framework is developed for three-dimensional swirl-stabilized flame response to non-axisymmetric disturbances. The dynamics are tracked using a level-set based G-equation applicable to infinitely thin flame sheets. For specific assumptions in a linear framework, general solution characteristics are obtained. The results are presented separately for axisymmetric and non-axisymmetric mean flames. The unsteady heat release process leads to an unsteady volume generation at the flame front due to the expansion of gases. This unsteady volume generation leads to sound generation by the flame as a distributed monopole source. A sound generation model is developed where ambient pressure fluctuations are generated by this distributed fluctuating heat release source on the flame surface. The flame response framework is used to provide this local heat release source input. This study has been specifically performed for the helical flow disturbance cases to illustrate the effects different modes have on the generated sound. Results show that the effects on global heat release and sound generation are significantly different. Finally, the prediction from the analytical models is compared with experimental data. First, a two-dimensional bluff-body stabilized flame experiment is used to obtain measurements of both the flow and flame position in time. This enables a local flame response comparison since the data are spatially resolved along the flame. Next, a three-dimensional swirl-stabilized lifted flame experiment is considered. The measured flow data is used as input to the G-equation model and the global flame response is predicted. This is then compared with the corresponding value obtained using global CH* chemilumenescence measurements.